A Wave-Mechanical Approach to Cosmic Structure Formation

The dynamical equations describing the evolution of a self-gravitating fluid can be rewritten in the form of a Schrödinger equation coupled to a Poisson equation determining the gravitational potential. This wave-mechanical representation allows an approach to cosmological gravitational instability that has numerous advantages over standard fluid-based methods. We explore the usefulness of the Schrödinger approach by applying it to a number of simple examples of self-gravitating systems in the weakly non-linear regime. We show that consistent description of a cold self-gravitating fluid requires an extra “quantum pressure” term to be added to the usual Schrödinger equation and we give examples of the effect of this term on the development of gravitational instability. We also show how the simple wave equation can be modified by the addition of a non-linear term to incorporate the effects of gas pressure described by a polytropic equation-of-state.